A Fracture Dynamics Model for Fiber Reinforced Ceramics

After fiber reinforced ceramics occur a crack, their fibrous position form bridging fibers, moreover a crack usually extends in the modality of similarity. In order to analyze facilely problems of fiber reinforced ceramics, bridging fiber segment is substituted for loads. A dynamic model of crack propagation is built and its fracture dynamics problems are researched by the approaches of self-similar functions. When a crack propagates at high speed its fiber continues to break. By application of the theory of complex functions, the problems dealt with can be easily translated into Remann-Hilbert problem. Using the built dynamic model and the ways of self-similar functions, analytical study of the displacements, stresses, dynamic stress intensity factor and bridging fibrous fracture velocity α under the action of a running constant force P and an running increasing load Pt, respectively, can be attained, and it is also utilized to obtain the concrete solution of the model by means of superposition theorem.